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Graphing from the derivative

Please sketch a graph of a function f have the indicated characteristics. Please explain.

(a) f(0) = f(2) = 0

f'(x) > 0 if x <1

f'(1) = 0

f'(x) < 0 if x > 1

f''(x) < 0

(b) f(0) = f(2) = 0

f'(x) < 0 if x < 1

f'(1) = 0

f'(x) > 0 if x > 1

f''(x) > 0

Solution Preview

Please find the attached solution.

Thanks

Differentiation
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Please sketch a graph of a function f have the indicated characteristics. Please explain.

(a) f(0) = f(2) = 0 f'(x) > 0 if x <1 f'(1) = 0

f'(x) < 0 if x > 1 f''(x) < 0

Solution :

f(0) = f(2) = 0 » The graph cuts the x-axis at those x-values. Hence our
graph passes through the x-axis at x = 0 and x = 2

f'(x) > 0 if x < 1 » First derivative means slope ... slope is positive , when our
graph at that region , ...

Solution Summary

This shows how to sketch graphs with the given characteristics of the derivative.

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